99 citations · 687 across the 54 of their papers we have counts for
5 papers · 1 filter
The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions
Todd A. Oliynyk
We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabo…
Stability of the (two-loop) Renormalization Group Flow for Nonlinear Sigma Models
Christine Guenther, Todd A. Oliynyk
We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model. To prove stability…
A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First Order
T. Oliynyk, V. Suneeta, E. Woolgar
Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target spac…
A Gradient Flow for Worldsheet Nonlinear Sigma Models
T Oliynyk, V Suneeta, E Woolgar
We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinea…
Irreversibility of World-sheet Renormalization Group Flow
T Oliynyk, V Suneeta, E Woolgar
We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in in string theory. Our techniques draw on the mathematics o…